The project focuses on development of efficient algorithms for finite automata applicable in formal verification and analysis of dynamic systems. The central idea is to explore connections between automata, SAT/SMT solving, and program verification. We believe that because all these three domains solve similar problems, interchanging ideas between the domains is possible and may significantly advance not only the domain of automata but also the other mentioned areas. The automata-based algorithms developed in the project will in particular target the following four lively domains of applications: analysis of string manipulating programs, shape analysis, verification of concurrent programs, and decision procedures of selected logics suitable for verification of infinite-state systems (such as WSkS or separation logic). The work on the project will include rigorous mathematical description of the developed principles and algorithms, as well as their implementation and experimental evaluation.